Option 21 DHS 3.1

Option 21 DHS 3.1

DHS - 3.1
№1.21. Four points are given A1 (1; –2; 7); A2 (4; 2; 10); A3 (2; 3; 5); A4 (5; 3; 7). Create equations: a) plane A1A2A3; b) straight A1A2; c) direct A4M; perpendicular to the A1A2A3 plane; d) straight A3N; parallel straight line A1A2; e) a plane passing through point A4; perpendicular to the straight A1A2; Calculate: e) the sine of the angle between the straight A1A4 and the plane A1A2A3; g) the cosine of the angle between the coordinate plane Oxu and the plane A1A2A3.
№2.21. Make a plane equation; which passes through the points M (1; 2; 3) and N (–3; 4; –5) parallel to the z axis.
№3.21. At what value are direct p; straight lines are parallel.